The Problem of Particle-Antiparticle in Particle Theory

Abstract

Following the results of our publications, in the first part of this letter, we explain that quantum theory based on finite mathematics (FQT) is more general (fundamental) than standard quantum theory based on Poincare invariance. Standard concept of particle-antiparticle is not universal because it arises as a result of symmetry breaking from FQT to standard quantum theory based on Poincare or standard anti-de Sitter symmetries. In FQT one irreducible representation of the symmetry algebra describes a particle and its antiparticle simultaneously, and there are no conservation laws of electric charge and baryon quantum number. Poincare and standard anti-de Sitter symmetry are good approximations at the present stage of the universe but in the early stages they cannot take place. Therefore, the statement that in such stages the numbers of baryons and antibaryons were the same, does not have a physical meaning, and the problem of baryon asymmetry of the universe does not arise. Analogously, the numbers of positive and negative electric charges at the present stage of the universe should not be the same, i.e., the total electric charge of the universe should not be zero.